On the elastic moduli and compliances of transversely isotropic and orthotropic materials

The relationships between the elastic moduli and compliances of transversely isotropic and orthotropic materials, which correspond to different appealing sets of linearly independent fourth-order base tensors used to cast the elastic moduli and compliances tensors, are derived by performing explicit inversions of the involved fourth-order tensors. The deduced sets of elastic constants are related to each other and to common engineering constants expressed in the Voigt notation with respect to the coordinate axes aligned along the directions orthogonal to the planes of material symmetry. The results are applied to a transversely isotropic monocrystalline zinc and an orthotropic human femural bone.